Atomic-Level Response of the Domain Walls in Bismuth Ferrite in a Subcoercive-Field Regime

The atomic-level response of zigzag ferroelectric domain walls (DWs) was investigated with in situ bias scanning transmission electron microscopy (STEM) in a subcoercive-field regime. Atomic-level movement of a single DW was observed. Unexpectedly, the change in the position of the DW, determined from the atomic displacement, did not follow the position of the strain field when the electric field was applied. This can be explained as low mobility defect segregation at the initial DW position, such as ordered clusters of oxygen vacancies. Further, the triangular apex of the zigzag wall is pinned, but it changes its shape and becomes asymmetric under electrical stimuli. This phenomenon is accompanied by strain and bound charge redistribution. We report on unique atomic-scale phenomena at the DW level and show that in situ STEM studies with atomic resolution are very relevant as they complement, and sometimes challenge, the knowledge gained from lower resolution studies.

The purity of the crystal has been confirmed by X-ray diffraction (Figure S1.1) and Raman Spectroscopy ( Figure S1.2).

Specimen preparation
The specimen is prepared on optimized Protochips-Fusion electrical Si-based chips with patterned electrodes by focused ion beam 1 (FIB) (Helios Nanolab 650 with Ga ions source). This type of FIB support chip 1 offers the possibility to prepare sufficiently thin, high-quality specimens in order to achieve atomic resolution while simultaneously applying electric field in situ.
A capacitor-like configuration offers the advantage of a relatively homogeneous electric field 2,3 , compared to other more frequently used configurations such as the probe techniques.
The first step of the specimen preparation was electron deposition of a thin layer of Pt (0.4 μm) which allow protection of the top surface of the sample before using the ion beam, which reduces ion implantation and improves sample quality. A next layer of Pt is further deposited with ions to create a thick protection layer for the FIB sample preparation process (2 μm). The sample is then milled using the ion beam to create a standing lamella which is then transferred with the aid of a manipulator on the biasing support chip.
The electrical contacts are made by ion beam assisted Pt-deposition (30 kV, ≈ 0.23 nA). The spacing between the electrodes is by default 20 μm.
A scanning electron microscopy (SEM) image of the specimen on the biasing chip is shown in Figure S2.1a. The specimen is thinned with ions until electron transparency is reached. To maintain mechanical stability, the specimen is not uniformly thinned. Some isolated windows with thickness less than 100nm are done (green color in Figure S2.1a), while the rest of the lamella is kept thicker ≈200 nm (blue color in Figure S2.1a). We always perform the in situ STEM analysis on areas where the domain structure is preserved and which are not thinner than 50 nm. In this way, the effects associated with the reduced thickness (reduction/annihilation of polarization, domain structure alteration) are avoided 4 .
Thinning of the specimen was done at 30 kV in 3 steps by progressively lowering the ion beam current (typically 0.8nA, 0.2nA and 8 pA). In addition, low energy ion beam cleaning is performed in order to gradually remove surface amorphization or any other kind of contamination.
The ion beam characteristics that we used for FIB lamella preparation are listed in the table below. In addition, a cut is made at the bottom of the specimen 2 to remove the material that was redeposited during ion milling and which may potentially be more conductive than the rest.
In order to check the amount of Ga contamination we performed energy dispersive X-ray analysis (EDXS) analysis. Quantitative EDXS/STEM mapping (Bi M, Fe K and Ga L lines shown in Figure   S2.2 a)-d)) was done across a BFO lamella prepared by FIB with the same conditions as the samples for in situ studies (a STEM dark field (DF) image is shown in Figure R1 e)). The EDXSmapping shows an inhomogeneous distribution of Ga throughout the lamella with the highest concentration on the top Pt-deposited layer, as expected. A line EDXS analysis on mid-section (red line marked in Figure S2.2 e)) shows that for the most part the concentration of Ga is around 1 wt% but increases very close to the edge because the specimen is mostly amorphous in this area.
The in situ experiments presented in the manuscript are done in regions of the sample which are mostly crystalline. Therefore, we would expect that the Ga concentration was around 1 wt%; we expect that a much smaller amount is incorporated in the perovskite lattice, most of the contamination should be set in the very thin amorphous sidewall. • Section 1 (pink): parts which are in direct contact with the electrodes and are relatively thick: 1.2 μm.
• Section 2 (green): electron transparent windows with thickness between 70 and 150 nm.   In the case of uncharged configurations (head-to-tail or tail-to-head configuration), in order to minimize the electrostatic and elastic energy, the walls usually lie on (or close to) the neutral plane, namely 71⁰ will lie on {110}pc, 109⁰ on {100}pc and 180⁰ on {110}pc [8][9][10][11] . No assumptions can be made about the crystallographic plane in which the charged DWs (head-to-head or tail-to-tail configuration) are lying.
We were able to assign the zigzag walls as being of 180˚-type: is antiparallel in one side compared to the other of the wall and the DW lays approximately on neutral {110}pc plane 10 ( Figure S3.1). They can be either 180˚ or 109˚ DWs. Previous studies 12 report this type of DWs to be ferroelastic so, the 109˚ DWs scenario is more plausible.

Figure S 3.2 (a) HAADF image of lamellar-like features. On each side of the lamellar-like features a close-up of 5x5 unit cells is shown, together with the overlapped Fe-displacement
vectors.  The direction of the electric field is indicated by arrows. The images correspond to the experiment shown in Figure 3 in the main manuscript. Each HAADF image is one individual frame.

Supplementary 6-Probing possible charged defects on the zigzag DWs.
Probing Bi vacancies.
The normalized Bi-column intensities were determined from HAADF images using a previously reported method 5,11 . The detector's background intensity is subtracted from the intensity of each pixel in the raw HAADF image. Further, the intensities of the atomic columns were extracted by the integration of the pixel values within one sigma, approximating a Gaussian-type intensity distribution.

O vacancies on zigzag DW
The O K edge intensity appears to be slightly lower in the DW location (marked with black line in Figure S6.5) compared to the domain matrix (marked with red line in Figure S6.5). The present result suggests probable segregation of O vacancies point charged defects at the zigzag walls.   is the angle between the , vectors and the wall plane DWI, DWII or apex.